Some two-step and three-step nilpotent Lie groups with small automorphism groups

Nilpotent Lie groups and hyperbolic automorphisms

A connected Lie group admitting an expansive automorphism is known to be nilpotent, but all nilpotent Lie groups do not admit expansive automorphism. In this article, we find sufficient conditions for a class of nilpotent Lie groups to admit expansive automorphism.

Anosov Automorphisms of Nilpotent Lie Algebras

Each matrix A in GL_n(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra on n generators. We study the relationship between the matrix A and the eigenvalues and rational invariant subspaces for f. We give applications to the study of Anosov automorphisms.

幂零群 $G$ 的自同构在 Sub_$G$ 上的远距作用及其在李群中格的应用

Distal Actions of Automorphisms of Nilpotent Groups $G$ on Sub_$G$ and Applications to Lattices in Lie Groups

本文研究了局部紧群自同构在闭子群空间上的远距作用，证明了幂零群和可解李群格上的远距性等价条件，并刻画了紧生成幂零群的结构。

On integrability of transverse Lie-Poisson structures at nilpotent elements

We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie-Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain completely integrable systems that consist of polynomial functions. We provide a uniform construction of these integrable systems for an infinite family of distinguished nilpotent elements of semisimple type.